Usually in monad tutorials, the = operator for the list monad is
defined as:
m = k = concat (map k m) -- or concatMap k m
but in the GHC sources it's defined as:
m = k = foldr ((++) . k) [] m
As far as I can tell, this definition is equivalent to the previous one
(correct me if
I run haskell on Mac OS X (Snow Leopard). After upgrading my Xcode
installation to 4.0 I had a tricky time getting ghc working again; the
version bundled with the Haskell Platform no longer works and I had to
compile a recent snapshot (ghc-7.1.20110315) from source. This worked
fine, but now
Hmm, it seems like MonadState can be derived even with a non-concrete
type, for instance:
--
{-# LANGUAGE GeneralizedNewtypeDeriving #-}
import Control.Monad.Error
import Control.Monad.State
import Data.Typeable
data SomeError =
Error1
| Error2
| ErrorFail
deriving (Eq,
I'm having a problem with a simple monad transformer stack that has me
stumped. Here's the sample code:
{-# LANGUAGE GeneralizedNewtypeDeriving #-}
import Control.Monad.Error
import Control.Monad.State
import Data.Typeable
data SomeError =
Error1
| Error2
| ErrorFail
deriving (Eq,
On 10/3/10 7:06 PM, Bryan O'Sullivan wrote:
On Sun, Oct 3, 2010 at 9:40 PM, Michael Vanier mvanie...@gmail.com
mailto:mvanie...@gmail.com wrote:
{- This doesn't work: -}
newtype MyMonad a =
MyMonad ((StateT (MyData a) (Either SomeError) a))
deriving (Monad
Hi everyone,
Here's some code that's giving me an error message I don't understand:
{-# LANGUAGE EmptyDataDecls,
MultiParamTypeClasses,
UndecidableInstances,
FlexibleInstances #-}
data Z
data S n
class Nat n where
toInt :: n - Int
instance Nat Z
On 8/24/10 1:54 PM, Bartek Æwik³owski wrote:
Hello Michael,
This is because instance selection is solely based on instance heads,
it doesn't consider contexts. There's a nice explanation available
here: http://www.haskell.org/haskellwiki/GHC/AdvancedOverlap
The fix in this case is very easy
Hi,
Quick question about ghci: when I do this at the prompt:
ghci :m +Control.Monad.Cont
I get
Ambiguous module name `Control.Monad.Cont':
it was found in multiple packages: mtl-1.1.0.2 monads-fd-0.0.0.1
Is there any way to fix this from within ghci (i.e. not involving
mucking
I stumbled across this monadic combinator:
mcombine :: Monad m = (a - a - a) - m a - m a - m a
mcombine f mx my = do
x - mx
y - my
return (f x y)
I used it to chain the outputs of two Parsec String parsers together
using this operator:
(++) :: Monad m = m String - m String - m
On 5/30/10 1:40 AM, Michael Snoyman wrote:
On Sun, May 30, 2010 at 11:35 AM, Michael Vanier mvanie...@gmail.com
mailto:mvanie...@gmail.com wrote:
I stumbled across this monadic combinator:
mcombine :: Monad m = (a - a - a) - m a - m a - m a
mcombine f mx my = do
x - mx
This is a great idea! IMO this is also one of the main ways that
GUI-based apps are likely to evolve into in the future. Cross-platform
GUIs are a pain in the butt in _any_ language (possibly excluding full
language platforms like Java/.NET, and I'll bet even those were a
nightmare for the
Matthias Görgens wrote:
A shining example are Dan Piponis blog posts. Not his fault, mind. All I see
is that there is something powerful. I also notice that the big brains
construct monads in many different ways and thus giving them entirely
different capabilities. An example of this is some
Hi everyone,
I'm interested in collecting good references for compiler optimizations
for functional languages (lazy, strict, statically-typed or not). Any
suggestions?
Thanks in advance,
Mike
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Awesome! Thanks, Don!
Mike
Don Stewart wrote:
mvanier42:
Hi everyone,
I'm interested in collecting good references for compiler optimizations
for functional languages (lazy, strict, statically-typed or not). Any
suggestions?
There's lots for what GHC implements on SimonPJ's
For a completely different approach, I've had good success running
xmonad from either Ubuntu minimal (which is a bare-bones version of
Ubuntu that few people realize exists) or Arch Linux. In either case
you have to spend more time setting up the system, but the results IMO
are worth it. I
jean-christophe mincke wrote:
Hello,
Has there already been attempts to introduce lisp like symbols in haskell?
Thank you
Regards
J-C
J-C,
Do you mean symbols as in interned strings with an O(1) string
comparison method? I would love to have those, but I don't see an easy
way to get
Gregory Collins wrote:
Tom Davie tom.da...@gmail.com writes:
On 10/31/09, Magicloud Magiclouds magicloud.magiclo...@gmail.com wrote:
After all, I never think OO as an oppsite way to all other things. The
idea is so general that if you say I cannot use it in Haskell at all,
that would
Hi everyone,
I ran into this error when recompiling some code I hadn't worked on in a
while:
Foo.hs:19:7:
Could not find module `Control.Monad.Error':
it was found in multiple packages: monads-fd-0.0.0.1 mtl-1.1.0.2
I gather that monads-fd is supposed to be a replacement for mtl, but
Matthias-Christian Ott wrote:
Hi,
usually I'm sceptical of programming languages which are not based
on the von Neumann architecture, but recently I got interested in
functional programming languages.
The arrogance of lots of Haskell users, who made me feel that using a
programming language
Simon Peyton-Jones wrote:
Haskell is a great language! Check out haskell.org. I'm ccing the Haskell
Cafe which is read by many people better qualified to answer your question than
me. (Since I've been working on Haskell for many years, I am not well
qualified to say how it seems to a
I've been trying to build ghc head from the darcs repo using these
instructions:
http://hackage.haskell.org/trac/ghc/wiki/Building/GettingTheSources
Unfortunately, when I do
./darcs-all --extra get
as described under Getting more packages it fails because the
darcs-all script doesn't
haonan21 wrote:
I'm very new to haskell hugs and would appreciate it if someone could help me
out here. I've been giving 2 questions.
1.) A and B are two sets of integers. Implement a function to obtain the
integers that belong to both sets.
Test your function fully.
2.) Define and test a
I've stumbled upon a structure that is like a weaker version of a monad,
one that supports return and but not =. Has anyone seen this
before, and if so, does it have a standard name?
Mike
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Tony Morris wrote:
Michael Vanier wrote:
I've stumbled upon a structure that is like a weaker version of a
monad, one that supports return and but not =. Has anyone seen
this before, and if so, does it have a standard name?
Mike
___
Haskell
Luke Palmer wrote:
On Tue, Apr 28, 2009 at 5:33 PM, Michael Vanier mvanie...@gmail.com
mailto:mvanie...@gmail.com wrote:
Tony Morris wrote:
Michael Vanier wrote:
I've stumbled upon a structure that is like a weaker version of a
monad, one that supports return
Hi,
I'm having a problem using Typeable with STRefs. Basically, I want to
store STRefs (among other things) in a universal type. STRef is an
instance of Typeable2, which means that STRef s a is Typeable if s and a
are both Typeable. The problem is that the state type s is opaque and I
can
by runST is RealWorld;
runST is just a pretty name for unsafePerformIO. So the state types
are actually the same, and the cast would succeed.
-- ryan
On Mon, Mar 16, 2009 at 5:48 PM, Michael Vanier mvanie...@gmail.com wrote:
Hi,
I'm having a problem using Typeable with STRefs. Basically, I want
FYI there is precedent for this kind of thing in the functional programming world. PLT Scheme has a
Scheme mailing list and also a Scheme-in-education mailing list, which tackles the problems of
trying to teach Scheme to new programmers. If you start such a mailing list for Haskell, I'd like
easier to
handle side-effecting computations.
Mike
Benjamin L.Russell wrote:
On Wed, 02 Jul 2008 00:58:08 -0700, Michael Vanier
[EMAIL PROTECTED] wrote:
FYI there is precedent for this kind of thing in the functional programming world. PLT Scheme has a
Scheme mailing list and also a Scheme
Actually, it's (+) for ints and (+.) for floats. Which kind of proves your
point.
Mike
Tim Docker wrote:
| An interesting critique of OCaml.
|
| http://enfranchisedmind.com/blog/2008/05/07/why-ocaml-sucks/
Interesting to me is that my pet ocaml peeve is not there: namely the
lack of
This is pure general waffle, but I saw the following comment on reddit.com
which impressed me:
C isn't hard; programming in C is hard. On the other hand: Haskell is hard,
but programming in Haskell is easy.
Mike
Simon Peyton-Jones wrote:
Friends
Over the next few months I'm giving two or
Bayley, Alistair wrote:
From: [EMAIL PROTECTED]
[mailto:[EMAIL PROTECTED] On Behalf Of Derek Elkins
(Not directed at gwern in particular)
I have a better idea. Let's decide to do nothing. The
benefits of this
approach are: 1) it takes zero effort to implement, 2) the number of
I haven't been following this thread closely, but would it be rude to suggest that someone who
doesn't want to put the effort into learning the (admittedly difficult) concepts that Haskell
embodies shouldn't be using the language? Haskell was never intended to be The Next Big Popular
Language.
Bernie Pope wrote:
On 12/11/2007, at 4:32 AM, Neil Mitchell wrote:
Hi
bear no resemblence to any machine-level constructs, and it seems
unthinkable that you could possibly write such a compiler in anything
but Haskell itself.
Hugs is written in C.
Really? :-.
Really :-)
I have a copy of COBOL for Dummies which I bought as a joke and have never
dared read.
Mike
[EMAIL PROTECTED] wrote:
Andrew Coppin writes:
Brent Yorgey wrote:
Expressiveness certainly makes it easier, but nothing (other than
sanity...) stops you from writing a Haskell compiler in,
It looks as if hoogle isn't working. I get 404s whenever I try to do any
search on hoogle.
Mike
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http://www.haskell.org/mailman/listinfo/haskell-cafe
In ghci, why does
throw $ ArithException DivideByZero
print
*** Exception: divide by zero
while
throwDyn $ ArithException DivideByZero
print
*** Exception: (unknown)
?
Mike
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Haskell-Cafe mailing list
Haskell-Cafe@haskell.org
Is there an implementation of a symbol type in Haskell i.e. a string which has a constant-time
comparison operation?
Mike
___
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Haskell-Cafe@haskell.org
http://www.haskell.org/mailman/listinfo/haskell-cafe
I'm thinking of a symbol type that can be used for a compiler, so a simple algebraic data type
wouldn't work. Unfortunately the GHC datatype isn't part of the GHC haskell libraries AFAICT.
Mike
Yitzchak Gale wrote:
Michael Vanier wrote:
Is there an implementation of a symbol type in Haskell
Hmm, I was hoping for something that didn't involve side effects.
Mike
Yitzchak Gale wrote:
Michael Vanier wrote:
I'm thinking of a symbol type that can be used
for a compiler...
Ah. Perhaps Data.HashTable is what you are looking
for then?
-Yitz
I haven't been following this discussion closely, but here's an idea: use
reverse psychology.
Haskell -- You're probably not smart enough to understand it.
Nothing like appealing to people's machismo to get them interested.
Mike
Seth Gordon wrote:
Aha! Instead of the lambda surrounded by
Define a merge function that merges two sorted lists into a sorted list containing all the elements
of the two lists. Then define the msort function, which will be recursive.
Mike
PR Stanley wrote:
Hi
Taken from chapter 6, section 8 of the Hutton book on programming in
Haskell:
5. Using
OK, you have the split function, and you have the merge function, and now you have to define the
msort function. First write down the base cases (there are two, as you mention), which should be
obvious. Then consider the remaining case. Let's say you split the list into two parts. Then what
APL is fairly obsolete now anyway. A more modern version of that language is J (www.jsoftware.com),
which does not use special characters. I've studied the language a bit, and it's quite interesting,
but it really doesn't offer much (anything?) over Haskell except a much terser notation and
It's very nice, but I would say that anyone who needs an elevator pitch shouldn't be using or
working with Haskell. Haskell is for people who already get it. I've had job offers from people
just because they knew I _liked_ Haskell, even though they weren't asking me to use it for the job.
Awesome!
I'm reminded of the IRC post that said that Haskell is bad, it makes you hate other
languages.
Mike
Dan Weston wrote:
And here's my guide for public health officials...
WARNING: Learning Haskell is dangerous to your health!
Disguised as a fully-functional programming language,
Xavier,
First off, we don't put the () after function names in Haskell.
What's happening is this (experts please correct any mistakes here):
1) You call prime on a number (e.g. 42).
2) In order to evaluate this further, (factors 42) must be evaluated at least
partially to give input to == in
snark
As you know, an arrow tutorial is like a wrapper around a monad tutorial, sort of like a container
around it that can do extra actions with sufficient lifting. The appropriate higher-order function
to convert monad tutorials to arrow tutorials will be left as an exercise to the reader.
For what it's worth, the nature of Haskell is such that you do (at least currently) have to spend a
lot of time reading research papers to understand what's going on. Maybe that will change sometime,
but probably not soon. This ties in to the open-endedness of Haskell; I sometimes think that
Hugh Perkins wrote:
I'm not trolling, despite strong appearances to the contrary ;-) My
primary objective/goal is to find a way to make threading easy. Thread
management today is like memory management in the early 90s. We kindof
had tools (new, delete in C++ for example) to do it. At
I can't agree with your point about Haskell being (just) a prototype language (assuming that's what
you meant). If that's the case, it won't last very long. Languages need to be something you can
write real, practical applications in. Fortunately, Haskell isn't just a prototype language. I'm
Of course, you can always do this:
data Nat = Zero | Succ Nat
but it's not very much fun to work with, and not very efficient.
Mike
David Roundy wrote:
On Thu, Aug 02, 2007 at 12:29:46PM -0700, brad clawsie wrote:
On Thu, Aug 02, 2007 at 12:17:06PM -0700, brad clawsie wrote:
as far as i
/lambdabot.html
shows it working on 6.4.1.
can it build under anything more recent?
t.
*Stefan O'Rear [EMAIL PROTECTED]*
Sent by: [EMAIL PROTECTED]
07/30/2007 11:59 PM
To
Michael Vanier [EMAIL PROTECTED]
cc
haskell-cafe@haskell.org haskell-cafe@haskell.org
Subject
O'Rear wrote:
On Mon, Jul 30, 2007 at 06:57:25PM -0700, Michael Vanier wrote:
When I try to build lambdabot, I get this:
Configuring lambdabot-4.0...
configure: Dependency base-any: using base-2.1.1
configure: Dependency unix-any: using unix-2.1
configure: Dependency network-any: using network
OK, Stefan was right. The arrows package is an extension of Control.Arrow, not a from-scratch
implementation. The name confused me. Perhaps a better name would be arrows-ext or something
like that.
Mike
Michael Vanier wrote:
Thanks, but this doesn't answer the question. I can load up
:
Module `Language.Haskell.Syntax' does not export `pling_name'
I'm using the latest darcs pull of lambdabot along with ghc 6.6.1. Anyone have
any ideas?
Thanks in advance for all the help,
Mike
Michael Vanier wrote:
OK, Stefan was right. The arrows package is an extension of
Control.Arrow
I submit my own attempts for consideration:
http://www.cs.caltech.edu/~mvanier/hacking/rants/cars.html
Mike
Andrew Coppin wrote:
From the guy who brought you data in Haskell is like an undead quantum
cat, I present the following:
If programming languages were like vehicles, C would be a
We always say that Haskell is named for Haskell Curry because his work provided the
logical/computational foundations for the language. How exactly is this the case? Specifically,
does anyone claim that Curry's combinatorial logic is more relevant to the theoretical foundations
of Haskell
Albert,
Thanks for the very detailed reply! That's the great thing about this mailing
list.
I find your description of seq somewhat disturbing. Is this behavior documented in the API? I
can't find it there. It suggests that perhaps there should be a
-0700, Michael Vanier wrote:
Albert,
Thanks for the very detailed reply! That's the great thing about this
mailing list.
I find your description of seq somewhat disturbing. Is this behavior
documented in the API? I can't find it there. It suggests that perhaps
there should be a really
That makes sense. Thanks!
Mike
Stefan O'Rear wrote:
On Thu, Jul 12, 2007 at 09:22:09PM -0700, Michael Vanier wrote:
I stumbled across a problem with IO and strictness that I could fix, but I
can't understand why the fix works. I've compressed it down into a program
which simply computes
I stumbled across a problem with IO and strictness that I could fix, but I can't understand why the
fix works. I've compressed it down into a program which simply computes the number of lines in a
file. Here is a version that doesn't work:
module Main where
import System.IO
import
I'm sure this has been done a hundred times before, but a simple generalization of foldl just
occurred to me and I wonder if there's anything like it in the standard libraries (I couldn't find
anything). Basically, I was trying to define the any function in terms of a fold, and my first
try
That's cool -- good point. takeWhile is also trivially defined in terms of
foldr:
takeWhile p = foldr (\x r - if p x then x:r else []) []
Can you do dropWhile in terms of foldr? I don't see how.
Mike
Stefan O'Rear wrote:
On Wed, Jul 04, 2007 at 04:20:20PM -0700, Michael Vanier wrote:
I'm
I noticed that both the Data.Array library and the Data.Map library use the (!) operator for
different purposes. How would it be possible to import both libraries usefully in a single module?
I guess what I'm really asking is: how do I qualify operator names?
Mike
That's pretty baa-aa-aad.
Mike
brad clawsie wrote:
On Wed, May 23, 2007 at 12:40:58PM -0700, Dan Weston wrote:
What power animal have you chosen for the cover of your O'Reilly book? Alas,
most of the good ones are gone already!
lamb-da?
___
I'm not sure what you mean by a lot of transcription work. It's an excellent book, aimed at
beginners.
Mike
PR Stanley wrote:
Hi
I've acquired a copy of the above title but it requires a lot of
transcription work. So, I thought I'd first ensure it's worth the time
and effort. This edition
The - in type signatures associates to the right, so the type signatures
fmap :: (a - b) - (W a - W b)
bind :: (a - W b) - (W a - W b)
are the same as:
fmap :: (a - b) - W a - W b
bind :: (a - W b) - W a - W b
Sometimes people put in the extra parentheses because they want to
emphasize a
the mindset of the masses - creating the
meme - that's tricky. Especialy if they're really off the B Ark!
(http://www.bbc.co.uk/cult/hitchhikers/guide/golgafrincham.shtml)
Neil
On 18/04/07, Michael Vanier [EMAIL PROTECTED] wrote:
R Hayes wrote:
On Apr 17, 2007, at 4:46 PM, David Brown wrote:
R
R Hayes wrote:
On Apr 17, 2007, at 4:46 PM, David Brown wrote:
R Hayes wrote:
They *enjoy* debugging ...
I have to say this is one of the best things I've found for catching
bad programmers during interviews, no matter what kind of system it is
for. I learned this the hard way after
For those of us who aren't type theorists: What's a negative datatype?
Mike
Edsko de Vries wrote:
Hey,
It is well-known that negative datatypes can be used to encode
recursion, without actually explicitly using recursion. As a little
exercise, I set out to define the fixpoint combinator using
P. R. Stanley wrote:
Brandon, Chris, Don,
gentlemen,
Thank you all for your swift and well-written answers.
I should point out that I'm coming to functional programming with a
strong background in programming in C and C-type languages. I am also
very new to the whole philosophy of functional
Brandon S. Allbery KF8NH wrote:
On Feb 18, 2007, at 21:44 , Michael Vanier wrote:
I think what you're asking here is why you need the parens around
(x:y) in the second case. Function application doesn't use parentheses
Function application never applies to pattern matching.
You're
P. R. Stanley wrote:
What are the pre-requisites for Lambda calculus?
Thanks
Paul
Learning lambda calculus requires no prerequisites other than the ability to
think clearly. However, don't think that you need to understand all about
lambda calculus in order to learn Haskell. It's more
FYI we teach and do a fair amount of functional programming here at Caltech. We
have courses using scheme, ocaml, and haskell with more on the way.
Mike
Greg Fitzgerald wrote:
Thomas,
Here's a good place to start, although I'm not sure how up to date it is:
Lennart,
Now you've made me curious. Which paper is this? Is it available for download
anywhere?
Mike
Lennart Augustsson wrote:
On Jan 29, 2007, at 03:01 , Alexy Khrabrov wrote:
How do people stumble on Haskell?
Well, I didn't really stumble on it. I was at the 1987 meeting
when we
Is there any support for multi-line string literals in Haskell? I've
done a web search and come up empty. I'm thinking of using Haskell to
generate web pages and having multi-line strings would be very useful.
Mike
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Haskell-Cafe mailing list
Yes, just like that ;-) Thanks!
Now if somebody has a string interpolation library, I'd be a pretty
happy camper ;-)
Mike
mvanier:
Is there any support for multi-line string literals in Haskell? I've
done a web search and come up empty. I'm thinking of using Haskell to
generate web
Excellent! Thanks.
Mike
Donald Bruce Stewart wrote:
Oh, like this (by Stefan Wehr):
http://www.cse.unsw.edu.au/~dons/code/icfp05/tests/unit-tests/VariableExpansion.hs
$ ghci -fth VariableExpansion.hs
*VariableExpansion let x = 7 in $( expand ${x} )
7
*VariableExpansion let url =
Date: Fri, 16 Sep 2005 23:33:46 +0200
From: Tomasz Zielonka [EMAIL PROTECTED]
On Fri, Sep 16, 2005 at 05:40:04PM +0100, Glynn Clements wrote:
Every other language (including Haskell) tends to have the problem
that eventually you will encounter a situation where the language's
own
From: Michael Vanier [EMAIL PROTECTED]
Date: Sat, 27 Aug 2005 22:06:40 -0700 (PDT)
Right now, the Debian unstable package for GHC 6.4 won't install due to
some conflict with libgmp3 (the package maintainer has been notified). I
tried to compile the sources from scratch but found out
From: Wolfgang Jeltsch [EMAIL PROTECTED]
Date: Sun, 28 Aug 2005 16:14:26 +0200
Am Sonntag, 28. August 2005 07:06 schrieb Michael Vanier:
Right now, the Debian unstable package for GHC 6.4 won't install due to
some conflict with libgmp3 (the package maintainer has been notified
Right now, the Debian unstable package for GHC 6.4 won't install due to
some conflict with libgmp3 (the package maintainer has been notified). I
tried to compile the sources from scratch but found out that GHC requires a
previously-existing version of itself to compile. I have hugs working
The explanation given below might be a bit heavy for someone who didn't know
much
about category theory. For those individuals I'd recommend Phil Wadler's
papers:
http://homepages.inf.ed.ac.uk/wadler/topics/monads.html
I especially recommend Monads for Functional Programming, The Essence of
I always thought Forth was way cool, but I've never managed to get anything
significant written in it. I think that Forth has echoes of the
point-free style in Haskell, but Haskell is a lot friendlier.
Is the Forth environment part of the hardware? If your Forth is just a
threaded interpreter
I came up with a terrible Haskell pun that I had to share with this list:
Haskell provides special syntactic support for monads in terms of the do
notation. There is a straightforward translation between this notation
and the core language, which constitutes its do-notational semantics,
Date: Wed, 11 May 2005 13:06:51 +0200
From: Jerzy Karczmarczuk [EMAIL PROTECTED]
Michael Vanier comments my defense of Matlab:
I used objects, and even a lot of functional
constructs. I don't see any reason to call it a creeping horror.
It is quite homogeneous and simple, and is decently
Date: Tue, 10 May 2005 19:02:33 -0400
From: Daniel Carrera [EMAIL PROTECTED]
Hello,
This might be a strange question to ask on a Haskell list, but I do want
to hear your opinions. What do you think of Python?
To explain where this question is comming from:
I have a lady friend who
From: Benjamin Franksen [EMAIL PROTECTED]
Date: Wed, 4 May 2005 22:47:21 +0200
On Wednesday 04 May 2005 22:22, [EMAIL PROTECTED] wrote:
Bryce Bockman writes:
Scheme is strict, so it lacks some of the flexibility (and drawbacks)
that come from Laziness, but in the book they teach you
Marcin gives a good capsule description of the differences between ocaml
and haskell. Let me add my two cents.
I also learned ocaml before learning haskell, and the biggest single
difference I found is that haskell is a lazy, purely functional language
and ocaml is a strict, mostly functional
Date: Sun, 13 Mar 2005 00:01:17 -0800
From: Sean Perry [EMAIL PROTECTED]
Cc:
Michael Vanier wrote:
Date: Sat, 12 Mar 2005 23:39:21 -0800
From: Sean Perry [EMAIL PROTECTED]
Cc: Haskell-Cafe@haskell.org
As an aside, I kept all of the exercises in revision control. So I can
look back
Date: Sat, 12 Mar 2005 23:39:21 -0800
From: Sean Perry [EMAIL PROTECTED]
Cc: Haskell-Cafe@haskell.org
As an aside, I kept all of the exercises in revision control. So I can
look back at what I first wrote and my later changes. A habit I plan to
keep as I move on to other programming
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